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4306/1H
Centre Number
Surname
Other Names
Candidate Signature
Candidate Number
General Certificate of Secondary EducationHigher TierJune 2010
Time allowed� 2 hours
Instructions� Use black ink or black ball-point pen. Draw diagrams in pencil.� Fill in the boxes at the top of this page.� Answer all questions.� You must answer the questions in the spaces provided. Do not write
outside the box around each page or on blank pages.� Do all rough work in this book. Cross through any work you do not
want to be marked.
Information� The marks for questions are shown in brackets.� The maximum mark for this paper is 100.� You may ask for more answer paper, graph paper and tracing paper.
These must be tagged securely to this answer booklet.
Advice� In all calculations, show clearly how you work out your answer.
Mathematics 4306/1H(Specification A)Paper 1 Non-calculator
Monday 7 June 2010 1.30 pm to 3.30 pm
(JUN1043061H01)
For this paper you must have:
� mathematical instruments.
You may not use a calculator.
H
WMP/Jun10/4306/1H
MarkPages
For Examiner’s Use
Examiner’s Initials
TOTAL
3
4–5
6–7
8–9
10–11
12–13
14–15
16–17
18–19
20–21
22
WMP/Jun10/4306/1H(02)
2
a
h
b
length
cross-section
Formulae Sheet: Higher Tier
4Volume of sphere = – π r 33
Surface area of sphere = 4π r2
1Volume of cone = – πr2h3
Curved surface area of cone = πrl
In any triangle ABC
1Area of triangle = – ab sin C2
a b cSine rule —— = —— = ——sin A sin B sin C
Cosine rule a2 = b2 + c2 – 2bc cos A
Volume of prism = area of cross-section × length
The Quadratic Equation
The solutions of ax2 + bx + c = 0, where a ≠ 0, are given by
– b ± √ (b2 – 4ac)x = ————————
2a
r
l
b a
c B
C
A
r
h
Area of trapezium = – (a +b)h12
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Answer all questions in the spaces provided.
1 A = –9 and B = 12
Work out the value of4(A + 3)
B
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Answer ...................................................................... (3 marks)
2 Jack has a box of 100 coloured discs.The discs are Red, Blue, Green and Yellow.The table shows some of the probabilities of choosing a colour.
2 (a) Jack chooses a disc at random from the box.Work out the probability that he chooses a Green disc.
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Answer ...................................................................... (2 marks)
2 (b) Jack says: ‘There must be 60 Red discs in the box.’
Is Jack correct?Tick the correct box.
Yes No
Give a reason for your answer.
Reason ..............................................................................................................................
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Colour Red Blue Green Yellow
Probability 0.6 0.1 0.1
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4
(04)
4 A flow diagram for a two-stage operation is shown.
4 (a) Fill in the boxes of the flow diagram so that they represent this two-stage operation.(2 marks)
4 (b) When the input is –1, what is the output?
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Answer ...................................................................... (1 mark)
3 The shape is a drawing of a house.
Work out the area of this shape.State the units of your answer.
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Answer ...................................................................... (4 marks)
8 cm
12 cm
6 cm
3 cm Not drawn accurately
2(n + 5)n
Input Output
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5 You are given that 46 × 137 = 6302
Write down the answers to these calculations.
5 (a) 46 × 1.37
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Answer ...................................................................... (1 mark)
5 (b) 6302460
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Answer ...................................................................... (1 mark)
5 (c) 6302046 × 137
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Answer ...................................................................... (1 mark)
Turn over for the next question
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10
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6 (a) Solve = 7
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Answer w = .............................................................. (1 mark)
6 (b) Solve 7x – 2 = 3x + 8
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Answer x = ............................................................... (3 marks)
6 (c) Solve 3y +11
= 24
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Answer y = ............................................................... (3 marks)
6
(06)
28w
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7 In the diagram AB is parallel to CD.
7 (a) Work out the value of x.
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Answer ........................................................ degrees (2 marks)
7 (b) Work out the value of y.Give a reason for your answer.
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Answer ........................................................ degrees
Reason .......................................................(2 marks)
Ay
x
B
C
105°
Not drawnaccurately
2xD
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9 Pam wants to collect information about the total number of hours of homework thestudents in her class did last week.
Design a suitable question she could use to find out this information.Remember to include response boxes.
Question ............................................................................................................................
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Response
(2 marks)
8 (a) Work out ÷
Give your answer in its simplest form.
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Answer ...................................................................... (3 marks)
8 (b) Work out 4 – 1
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Answer ...................................................................... (3 marks)
8
(08)
56
34
25
13
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10 The diagram shows a regular octagon.
10 (a) Explain why the exterior angle of a regular octagon, marked x on the diagram, is 45°
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10 (b) The diagram shows part of a regular polygon.Each interior angle is 168°.
Calculate the number of sides of this regular polygon.
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Answer ...................................................................... (3 marks)
9
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168° 168°
168° 168°
Not drawnaccurately
x
Not drawn accurately
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11 A restaurant offers a family discount.The Taylor family have a meal at this restaurant.Before the discount the meal costs £140After the discount the cost is £112
Calculate the percentage discount.
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Answer .................................................................. % (3 marks)
12 (a) Complete the table of values for y = x2 – 4x + 2
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12 (b) On the grid opposite, draw the graph of y = x2 – 4x + 2 for values of x from –1 to 5(2 marks)
12 (c) Use the graph to solve the equation x2 – 4x + 2 = 0
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Answer x = ......................... or x = ........................ (1 mark)
x –1 0 1 2 3 4 5
y 2 –1 –1 2 7
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8
–1 O
–1
–2
1
2
3
4
5
6
7
1 2 3 x
y
4 5
–3
8
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13 These five numbers are written in standard form.
4.5 × 105 8.7 × 100 6.9 × 10–3 3.2 × 106 1.8 × 10–1
13 (a) Write down the smallest number.
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Answer ...................................................................... (1 mark)
13 (b) Write down the largest number.
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Answer ...................................................................... (1 mark)
13 (c) Write 1.8 × 10–1 as an ordinary number.
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Answer ...................................................................... (1 mark)
13 (d) Work out 4.5 × 105 × 0.01 Give your answer in standard form.
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Answer ...................................................................... (2 marks)
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14 Triangles ABC and DEF are similar.Angle ABC = angle DEF.
14 (a) Work out the size of angle DEF.
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Answer ........................................................ degrees (2 marks)
14 (b) Calculate the length of DF.
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Answer ................................................................ cm (3 marks)
13
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10
EDB28º
20 cm
F
A
37º
C
15 cm8 cm
Not drawn accurately
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15 The table shows the profits of a small business during each quarter from March 2008to June 2009. The March 2009 entry is missing from the table.
15 (a) Calculate the first four-point moving average.
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Answer £ .................................................................. (2 marks)
15 (b) The second four-point moving average is £28 000
Calculate the missing entry for March 2009.
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Answer £ .................................................................. (2 marks)
14
(14)
Date Mar 08 June 08 Sept 08 Dec 08 Mar 09 June 09
Profits 38 000 29 000 25 000 34 000 21 000
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16 (a) Show clearly that (x + 5)(x – 2) + 3 (x + 1) ≡ x2 + 6x – 7
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16 (b) Factorise x2 + 6x – 7
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Answer ...................................................................... (2 marks)
16 (c) Hence, or otherwise, solve (x + 5)(x – 2) + 3 (x + 1) = 0
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Answer ...................................................................... (2 marks)
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17 (a) Factorise fully 6x2 – 10xy
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Answer ...................................................................... (2 marks)
17 (b) Simplify (5a4b)3
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Answer ...................................................................... (2 marks)
18 Evaluate 810.5 × 6–2
Give your answer in its simplest form.
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Answer ...................................................................... (3 marks)
16
(16)
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19 The diagram shows the graph of y = x2 + bx + c
Find the values of b and c.You must show all your working.
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Answer b = ........................ , c = ........................... (3 marks)
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10
14
2 7
y
x
Not drawn accurately
O
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20 A data logging machine in a car park records the length of time that cars are parked.Here are Monday’s results, along with the parking charges.
Monday’s results are equivalent to a 20% sample for the whole week, stratified by thefour time intervals.
Work out the car park takings for the whole week.
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Answer £ .................................................................. (3 marks)
18
(18)
Length of time (hours) Number of cars Charge (£)
0 – 1 90 1.20
1 – 2 130 2.00
2 – 3 80 3.50
more than 3 60 5.00
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21 A tennis ball of radius r is packaged in a cylindrical box.The ball touches the sides, top and base of the box.
What fraction of the volume of the box is empty space?You must show all your working.
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Answer ...................................................................... (4 marks)
19
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7
r
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w × 822 Find the value of w if ———– = 2 33
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Answer ...................................................................... (3 marks)
23 Solve the equation x2 – 4x – 15 = 0
Give your answers in surd form in their simplest form.
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Answer ...................................................................... (3 marks)
20
(20)
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24 ABCD is a cyclic quadrilateral.AE is a tangent at A.CDE is a straight line.Angle CAD = 32°Angle ABD = 40°
Work out the size of angle AED, marked x, on the diagram.You must show your working.Give reasons for any angles you work out.
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Answer ........................................................ degrees (5 marks)
21
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B C
D
AE
x
32 º
40 º
Not drawn accurately
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25 Emilia picks a chocolate at random from a box.All the chocolates in the box are identically wrapped.
The probability that she picks a caramel is
Sophie picks a chocolate at random from a different box.All the chocolates in Sophie’s box are identically wrapped.The probability that she picks a caramel is denoted by p.
The probability that both Emilia and Sophie pick a caramel is
25 (a) Work out the value of p.
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Answer ...................................................................... (2 marks)
25 (b) Calculate the probability that neither Emilia nor Sophie picks a caramel.
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Answer ...................................................................... (2 marks)
END OF QUESTIONS
22
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4
14
58
Emilia’s box
P (Emilia picks a caramel) =58
Sophie’s box
P (Sophie picks a caramel) = p
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